My thoughts:
Other options:
Defensive balance:
Give the drones immunity to speed boost, so they're not double speed on your planets?
Cap their attack boost?
Offensive balance:
Increase the metal value of drones, to increase reprisal intensity from using them a lot to something meaningful?
Some of all this might also apply to the combat carrier, but that should probably be a little more favoured balance wise as it's a bonus ship.
Responses:
For the cooldown issue, I would lean towards build points over time, as this seems less... well, artificial, and can be balanced separately from survivability.
With regards to the drone types, I'm not sure whether this solves the problem or not- if the amount of drones is the same, why not just have one enclave of each type, and sidestep the issue at the cost of micro? On ultra-low caps 1HW, you can't do this without unlocking more, as I think you only get 2 per homeworld, but in an other case you can mix and match- and if one type of ship in particular is the problem, this could end up buffing enclaves. Maybe one drone type should outright go?